Let $f (x) = x^{2}$ and $g (x) = 2 x + 1$ be two real functions. Find $(f + g) (x), (f - g) (x), (f g) (x), (\frac{f}{g}) (x) .$

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Solution

$(f + g) (x) = f (x) + g (x)$

$= x^{2} + 2 x + 1$

$(f - g) (x) = f (x) - g (x)$

$= x^{2} - (2 x + 1)$

$= x^{2} - 2 x - 1$

$(f g) (x) = f (x) . g (x)$

$= x^{2} (2 x + 1)$

$= 2 x^{3} + x^{2}$

$(\frac{f}{g}) (x) = \frac{f (x)}{g (x)}$ $(g (x) \neq 0)$

$= \frac{x^{2}}{2 x + 1}$ $(x \neq - \frac{1}{2})$

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